Calculating device



C. R. NICHOLS CALCULATING DEVICE Filed Oct. 19. 1923 1N VEN TOR ZM 7l?ZM f, A TTOR NE YS' Jan. 10, 1928.

3 Sheets-Sheet 2 INVENTOR C. R. NICHOLS CALGULATING DEVICE Flled Oct 19,1923 Jan. 10, 1928.

Jan. 10, 1928. 1,655,819

c. R. NICHOLS CALCULATING DEVI CE Filed Oct. 19, 1923 5 Sheets-Sheet 5ym i A A and C corresponds to 64 on from the same distance as the point2 is on scales A and C and similarly the point 8 on B. To multiply twoby eight the line L is run through 2 on scale A or C and through 8 onscale C or A; in either case it will intersect scale B at 16. To divide16 by 2 or 8 the line L is run through 16 on-B and through 2 -on` A- orC or 8 on A'or C the result 8 or 2 being read oli' in either case on Cor A.

The arrangement of single line scales above set forth is advantageous inpermit- V tingcalculations to be made by a single setparallel lines withthe in sequence from the line ,to 'the end of the last, the totaleffective ting of a single straight line member and in accordance withthe principle of this invention the scales A, B and C may be lengthenedto any desired extent and divided into sections togive the utmostaccuracywithin conveniently limited space in setting and reading figuresinvolving4 adarge number of significant figures or decimal places. Asshown in Fig. 2 the scales A and C are composed of a series of sectionsarranged as,

scale divisions marked beginning of the first length of each scale beingthe sum of its secf tions between lines 0-0 and Q -Q- Thus witheighteenlines (asshown in Fig. 2) the size ot the modulus for the scaleused is eighteen times as large as the modulus for a single linebetween-lines 0-0 and Q-Q and the accuracy of the readings 1scorrespondingly increased; The scale B is also correspondingly dividedinto eighteen sections numbered 2, 4, has auxiliaryintermediate sectionsunevenly numbered 3, 5, 7, etc., to 35. Each'evenly numbered section 2,4, etc., of scale B is half way between an evenly numbered line on scaleA and an evenly numbered line on scale C or between an unevenly numberedl1ne on scale A and an unevenly numberedy line on scale C. Each unevenlynumbered section of scale'B falls half way between an evenly numberedline of scale A and an unevenly numbered line of scale C 'or between anunevenly numbered line of scale A and an evenly numbered line of scale CThusL for every pair of lines, one from scale A and one from scale C',there is an intermediate line of scale B exactly half way between themand-numbered asthe sum of the number of the line of scale A. plus theninnber of the line of .scale C,'thus making a l sub-combination ofthree equally spaced parallel lines diagrammatically explained inconnection with Fig. 1. The modulus of the scale B is (asin B of Fig. 1)on'half ofs that of the scales A and C so `that its unit `is half aslarge and its numbers are the 4squares of the correspondingly placednumbers of scales A and C. The sections 1-18 o f scales A and C` areeachstarted from line 0' as equal length segments ra-ken con- 6, 8, 10,etc., to 36 and 'secutively along the scale but it is not-neces-- ilarlythek sections may for convenience be irregularly extended at their upperand lower ends to complete desired divisions, as shown injFig. 2. Thelines 2, 4-36 of scale B are similarly formed with the one half modulussca-le starting with 1() corresponding to -logarithmic mantissa 0 atpoint BO; and the lines 3, 5-'-35 of scale B are similarly formed withthe one half modulus scale starting from point Bx at the point of thescale corresponding to the linear midpoint p., ot the first line (2)ofscale B. In

the example given in Fig. 2 this midpoint is 11377. lith this method offorma-tion it is obvious that each lline 3. 5-35 of scale B begins atthe linear middle point of the preceding section 2, 4-34 duplicating atthe bottom the upper half of said preceding section. These lines 3,5--35 nlay be said to be fitted between the lines 2, 4-36 and at the topduplicating the lower half of the succeeding section 4, 6-36. It is notnecesy sary that the sections of a scale shall be equidistant. They mustfollowl some regular system of spacing of course'but might, for example,have the distance between sections decrease or increase from left toright.

`Length of segments need not be lconstant either.

Tn using this device for instance to multiply 26 by 312 the left'end ofstraight line L may be placed on point 26 of line v8 of scale A and theright end of line L on point 312 of line 9 of'scale C and the result8112 will be read to all four places online 8+9 or line 1T, of scale B-on a chart in which the scale sections are eighteen inches inV height.On the lower portions of such a,

scale it is possible to. read'the result to five and/ even six figureswith accuracy.

lIn. determining the line of scale B which mustbe looked to for theresult of any given operation the above method'utilizes the sum of thenumbers of thelines on A and C. This computation may be dispensed withby constructing the device providing the straight line relation' L so asto automatically 'indicate the proper line on scale B. For instance inFigs. 3. and 4 the straight bar r may havefixed lines@ for scale A andlines 7) and o on slides sb andsc liltl' for scales B and Crespectively. These slides are threaded onto a shaft t having a. helicalscrew thread of one pitch for slide se and another thread of 4halt` thispitch for slide sb. With the slidet sb set so that its lines b aremidway between lines a and c then-this relation is maintained for allsettlrlgs of the slide a, With this device the some desired Aregularends ot lines a, 7);'10 are in the same straight line and line b willalways indicate to the result on scale 1B or the line c will indicatethe result on scale'c in inverse operations. l

Another device Jfor accomplishing this result is shown in Figs. threelenses la, 1b, 1c always kept equidistant and in the same straight lineby linkages che, ,t and g pivoted together so as to permit the lenses tobe spread to the desired tigures on the chart. Fach lens carries markingindicating the central point of the lens and whenany two lenses arepositioned on their respective numbers ot a` problem the third lens willby its point indicate the third number or angle to which is the resultdesired. 1

Scales A and C do not have to have the same modulus'and the relativespacing ot the scales A, B, C may be altered so as to give a l to 2 or`l to 3 or any other instead of the simpler l to l ratio adopted in theabove examples, and the markings et any or all of the scales may insteadof numbers be in terms of trigonometric functions, angles, logarithms orany other systemv adapted for special use. Various auxiliary scales mayalso beadded for instance to give higher pewers'and roots or otherfunctions of the systems of scales A, B, C. For example addingalog logscale (the logarithm of the logarithm et a number) -to scale C willenable us to read any roots and any powers of numbers. F or leg a equalsn. log Then log (n log equals log n plus log log 'llhen et n on scalel Aand on the log log scale on C and read the result (aan) on scale C.lnvert the operation to read roots. @ther uscales l), E might becombined with the scales shown (see Fig. 2), scale D might lie to theleft ot A for instance and l to the right of C. on scales D and l@ maythen be read .from scale B. '0r auxiliary scale D may la above A. whilescale E lies below C and again theresults of calculation on the-scales'A l) and Fi will be read oil on the scale The; segments ot'- thelogarithmicscales may be arranged at `right angles'to the segments asshown in Fig. 2, this being Iequivalentto placing scale A above thescale l andscale C belowscale B. Or the scales might each be turnedthrough a certain angle such as 45 or a combination of any of thesearrangements might be used which would permit using a. number ofspecialfunctlonal scales in combination. ln any of these cases the chartwould function exactly as before,

relation being mainltained between the lines of the respective scales.

ln Figs. 8, 9 and 10 further and preferred embodiments of the inventionare shown involving a super-position of logarithmic scales 5 and 6,providing- Fig. 8 so as to rlhe results of calculations on the otherside of the linea. Calculations are placed can be made in exactly thesame manner as upon the chart shown in Fig. 2, since the product oitwonumbers always lies half way between the two numbers. ln using the threelens arrangement for a reading device` as shown (Fig. S) for instance tomultiply 5 by 6 the product 3() will be read oil on the cenlral lens butin order to multiply two numbers that are very close together, itisneces` sary to duplicate the set of scales shown in provide two suchsets of scales ride by side, then any desired calculation maybe providedtor and the device as a whole will occupy. only about two thirds oi thespace occupiedA by the three scales of Fig. 2.

Il. straight line embodiment of the principles ot the invention is shownin Fig. l). From c to (Z in this device of Fig. 9 a logarithmic scale A1arithmic scales B1 and B2 of one halt the modulus .ot scale A'. lf twonumbers to be multiplied are set olf on scale A l their product can beread from scales B1, B2 at a point half way lbetween the two numbers tobe multiplied. Thus2 5=10 in the example shown in the drawing. scalesA1, l31 and B2 are duplicated at A1', B1 and B2. to enable two numbersof nearly the same value to be set od on .scales A1, A1"

by means of the three lens device. l ln this case also the product of4the two numbers is provided below two log--` From ci to e thel can beread olf from the scales B1, B2, B1',

B2 at a point one half way between the numbers. Frein e to fthe sc alesB1, ll, are repeated and the lower divisions of scale A2 are marked oli'as the signs oll angles instead of numbers. From f to g the scales B1and B2 are repeated andscale A, ismarked .oit as the tangents of angles.lt 1s, of course.

of scales B1,

not necessary that the modulus B2, B1', B2 be one halt of the modulus ofscale A1. Changing the ratio of the'two moduli meanschangingthepositiomot the middle lens accordingly. ln Fig. l0 the straight linedevice of Fig. 9 is snown cut into segments arranged side by side inparallel compact term, there being, of course, two lines for the scalesB1, B2 for each line of the scale A1. lfthe modulus of scale B1, B2 weretwo thirds of the modulus of scale A1, instead of one half, itA would benecessary to have two instead of one intermediate segment between eachpair of segments of scale Al and the middle lens of the three lensdovice would be spaced from the left lens a distance equal to'tWo thirdsof the distance -be-v tween the two opposite lens.

Another embodiment of apparatus utilizing the principles of thisinvention is shown in Figs. 11 and- 12 in whichv the three rollers X, Y,Z are arranged side by side With theirl axes parallel. Each roller X, Y,Z has Wrapped around its cylindrical surface a scale corresponding toscale A, Bor C respectively, the segments of each scale being parallelto the axis of the roller on which it is wound. A and C', the propersegment on scale B being determined by adding the numbers of thesegments usedeon scales A' and C and the result read by means ot a hail'line as in Fig. l. The three rollers X, Y, Z are preferably intergeared,as indicated, by differential mechanism W, so that the proper segment onthe third automatically brought to the front when the other two rollersare rotated.

I claim l l. A calculating device comprising a plurality of logarithmicscales eachlcomprising a series of parallel line sections of the samescale, and a member adapted to move to various angular positions withrespect to said scales and adapted to indicate in a single position thecalculation and the result of the calculation.

2. A calculating device comprising a plurality of logarithmic scaleseach comprising a series of parallel line sections of the same scale,and a member adapted upcn relative movement between said scales tovarious angular positions With respect to' said scales and adapted toindicate in a single position the calculation and the result of thecalculation. f

3. A calculating device comprising a plurality of logarithmic scaleseach comprising l a series of parallel line sections of the same scale,a scale between said plurality of sca-les, and a movable member adaptedto move to various angular positions With respect to said rst mentionedscales and adapted to indicate in a single position the calculation andthe result of the calculation at a point on said scale between saidlirst mentioned scales.

4. In ya calculating Numbers can be set on scales scale will always beObered parallel lines,

device the coinbination with a plurality comprising a plurality ofparallel equally spaced straight line sections of the same scale, of asingle member movable to different positions on said scales and havingindicating means intersecting the result comprising means forpermanently maintaining three points in a straight line.

5. In a calculating device the combination with a plurality of scaleseach scale comprising a plurality of parallel` equally spaced straightline sections ot' the same scale, ot a member movable to dierentpositionson said scales and having indicating means automatically movingto point to the result When said member is positioned to indicate thecalculation on said scales.

6. In a calculatingdevice the combination prising a plurality ofparallel equally spaced straight line sections of the same scale, of amember movable to diierent angular positions on said scales and havingindicating` means intersecting the result when said member is positionedto indicate the calculation on said scales.

7. In a calculating device the combination with a plurality of scaleseach scale comprising a plu 'ality of parallel equally spaced straightline sections of the same scale, of a member movable to dierent angularp0- sitions on said scales and having indicating means automaticallymoving to point to the result.

8. In a calculating device the combination with .scales each comprisinga series of numbered parallel lines, of a member adaptedto be set -vvithrelation to noints on certain lines of said scales and automaticallyintersecting the result on another of said4 scales at a line thereonnumbered in a manner corresponding to the setting of said member on saidpoints.

9. vIn a calculating device the combination with scales each comprisinga series of-numof a member adapted to be set With relation to points oncertain lines of said scales and automatically intersecting the resulton another of said .scales at a line thereon numbered to be the sum otthe numbers of the 'lines containing mentioned points.

CHARLES RODNEY NICHOLS.

of scales each scale said first with a plurality of scales each scalecomk

